Lattice $\mathcal{N}=1$ super-Yang-Mills formulated using Ginsparg-Wilson fermions provides a rigorous nonperturbative definition of the continuum theory that requires no fine-tuning as the lattice spacing is reduced to zero. Domain wall fermions are one explicit scheme for achieving this and using them we have performed large-scale Monte Carlo simulations of the theory for gauge group SU(2). We have measured the gaugino condensate, static potential, Creutz ratios, and residual mass for several values of the domain wall separation $L_s$, four-dimensional lattice volume, and two values of the bare gauge coupling. With this data we are able to extrapolate the gaugino condensate to the chiral limit, to express it in physical units, and to establish important benchmarks for future studies of super-Yang-Mills on the lattice.

We show that the requirement of gauge invariance is not enough to fix the form of interactions between unparticles and gauge fields, thus revealing a wide new class of gauged unparticle actions. Our approach also allows us to construct operators which create gauge invariant colored unparticles. We discuss both their perturbative and nonperturbative properties.

We explore the characteristics of spherical bags made of large numbers of BPS magnetic monopoles. There are two extreme limits. In the Abelian bag, $N$ zeros of the Higgs field are arranged in a quasiregular lattice on a sphere of radius $R_{\mathrm{cr}}\sim N/v$, where $v$ is the Higgs vacuum expectation value. The massive gauge fields of the theory are largely confined to a thin shell at this radius that separates an interior with almost vanishing magnetic and Higgs fields from an exterior region with long-range Coulomb magnetic and Higgs fields. In the other limiting case, which we term a non-Abelian bag, the $N$ zeros of the Higgs field are all the origin, but there is again a thin shell of radius $R_{\mathrm{cr}}$. In this case the region enclosed by this shell can be viewed as a large monopole core, with small Higgs field but nontrivial massive and massless gauge fields.

The Mann-Marolf surface term is a specific candidate for the “reference background term” that is to be subtracted from the Gibbons-Hawking surface term in order make the total gravitational action of asymptotically flat spacetimes finite. That is, the total gravitational action is taken to be: $(\mathrm{\text{Einstein}}\mathrm{\text{−}}\mathrm{\text{Hilbert}}\mathrm{\text{bulk}}\mathrm{\text{term}})+(\mathrm{\text{Gibbons}}\mathrm{\text{−}}\mathrm{\text{Hawking}}\mathrm{\text{surface}}\mathrm{\text{term}})-(\mathrm{\text{Mann}}\mathrm{\text{−}}\mathrm{\text{Marolf}}\mathrm{\text{surface}}\mathrm{\text{term}})$. As presented by Mann and Marolf, their surface term is specified implicitly in terms of the Ricci tensor of the boundary. Herein, I demonstrate that, for the physically interesting case of a ($3+1$)-dimensional bulk spacetime, the Mann-Marolf surface term can be specified explicitly in terms of the Einstein tensor of the ($2+1$)-dimensional boundary.

We explore the feasibility and astrophysical consequences of a new long-range $U(1)$ gauge field (“dark electromagnetism”) that couples only to dark matter, not to the standard model. The dark matter consists of an equal number of positive and negative charges under the new force, but annihilations are suppressed if the dark-matter mass is sufficiently high and the dark fine-structure constant $\widehat{\alpha }$ is sufficiently small. The correct relic abundance can be obtained if the dark matter also couples to the conventional weak interactions, and we verify that this is consistent with particle-physics constraints. The primary limit on $\widehat{\alpha }$ comes from the demand that the dark matter be effectively collisionless in galactic dynamics, which implies $\widehat{\alpha }\lesssim {10}^{-3}$ for TeV-scale dark matter. These values are easily compatible with constraints from structure formation and primordial nucleosynthesis. We raise the prospect of interesting new plasma effects in dark-matter dynamics, which remain to be explored.

We reconsider the two different facets of $\pi$ and $K$ mesons as $q\overline{q}$ bound states and approximate Nambu-Goldstone bosons. We address several topics, including masses, mass splittings between $\pi$ and $\rho$ and between $K$ and $K^{*}$, meson wave functions, charge radii, and the $K-\pi$ wave function overlap.

Relating the effective Lorentz violation coefficients for composite particles to the coefficients for their constituent fields is a challenging problem. We calculate the Lorentz violation coefficients relevant to the dynamics of an $\alpha$ particle in terms of proton and neutron coefficients. The $\alpha$-particle coefficients would lead to anisotropies in the $\alpha$ decays of nuclei, and because the decay process involves quantum tunneling, the effects of any Lorentz violations could be exponentially enhanced.

We construct two sets of twist-3 correlation functions that are responsible for generating the novel single transverse-spin asymmetry in the QCD collinear factorization approach. We derive evolution equations for these universal three-parton correlation functions. We calculate evolution kernels relevant to the gluonic pole contributions to the asymmetry at the order of ${\alpha }_s$. We find that all evolution kernels are infrared safe as they should be and have a lot in common with the Dokshitzer-Gribov-Lipatov-Alterelli-Parisi evolution kernels of unpolarized parton distributions. By solving the evolution equations, we explicitly demonstrate the factorization scale dependence of these twist-3 correlation functions.

A study of the effective $tbW$ vertex is done in the littlest Higgs model with $T$ parity that includes the one-loop induced weak dipole coefficient $f_{2R}$. The top’s width and the $W$-boson helicity in the $t\to b{W}^{+}$ decay as well as the $t$-channel and the $s$-channel modes of single top quark production at the LHC are then obtained for the $tbW$ coupling. Our calculation is done in the Feynman-’t Hooft gauge, and we provide details of the analysis, like exact formulas (to all orders of the expansion variable $v/f$) of masses and mixing angles of all of the particles involved. Also, a complete and exact diagonalization (and normalization) of the scalar sector of the model is made.

We study the mixing of photons with hypothetical massive spin-two particles in the presence of a magnetic field. Mixing phenomena have been studied in the case of axionlike particles and strictly massless spin-two particles (gravitons) but not in this case. We find several interesting differences between them.

The search for supersymmetry and other classes of new physics will be tackled on two fronts, with high energy, direct detection machines, and in high-precision experiments searching for indirect signatures. While each of these methods has its own strengths, even more can be gained by finding ways to combine their results. In this paper, we examine one way of bridging these two types of experiments by calculating sum rules which link physical squark masses to the flavor-violating squark mixings. These sum rules are calculated for minimally flavor-violating supersymmetry theories at both high and low $\tan \beta$. We also explore how the sum rules could help to disentangle the relative strength of the gluino contributions to $b\to s\gamma$, a favored channel for indirect searches of new physics.

We compute a formula including operator-product expansion power corrections to describe the running of a QCD coupling nonperturbatively defined through the ghost and gluon dressing functions. This turns out to be rather accurate. We propose the “plateau” procedure to compute ${\Lambda }_{\overline{\mathrm{MS}}}$ from the lattice computation of the running coupling constant. We show a good agreement between the different methods which have been used to estimate ${\Lambda }_{\overline{\mathrm{MS}}}^{N_f=0}$. We argue that ${\Lambda }_{\overline{\mathrm{MS}}}$ or the strong coupling constant computed with different lattice spacings may be used to estimate the lattice spacing ratio.

We demonstrate that in the region of Bjorken $x_{\mathrm{Bj}}\sim m_{\pi }^2/(4\pi F_{\pi }{)}^2$ and/or $x_{\mathrm{Bj}}\sim |t|/(4\pi F_{\pi }{)}^2$ the standard $\chi \mathrm{PT}$ for the pion generalized parton distributions (GPDs) fails and one must perform all order resummation of $\chi \mathrm{PT}$. We perform such resummation in the large-$N$ limit of the $O(N+1)$ extension of the chiral theory. Explicit resummation allows us to reveal novel phenomena—the form of the leading chiral correction to pion parton distribution functions (PDFs) and GPDs depends on the small $x$ asymptotic of the pion PDFs. In particular, if the pion PDF in the chiral limit has the Regge-like small $x$ behavior $q(x)\sim 1/x^{\omega }$, the leading large impact parameter ($b_{\perp }\to \infty$) asymptotics of the quark distribution in the transverse plane has the form ($m_{\pi }=0$) $q(x,b_{\perp })\sim 1/x^{\omega }{ln}^{\omega }(b_{\perp }^2)/b_{\perp }^{2(1+\omega )}$. This result is model independent and it is controlled completely by the all order resummed $\chi \mathrm{PT}$ developed in this paper. This asymptotic interweaves with small-$x$ behavior of usual PDFs, hence it depends on the scale, at which the corresponding PDF is defined. This is a new and interesting result in which the chiral expansion meets the QCD evolution.

Operators in $\mathcal{N}=4$ super Yang-Mills theory with an $\mathcal{R}$-charge of $O(N^2)$ are dual to backgrounds which are asymtotically ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$. In this article we develop efficient techniques that allow the computation of correlation functions in these backgrounds. We find that (i) contractions between fields in the string words and fields in the operator creating the background are the field theory accounting of the new geometry, (ii) correlation functions of probes in these backgrounds are given by the free field theory contractions but with rescaled propagators and (iii) in these backgrounds there are no open string excitations with their special end point interactions; we have only closed string excitations.

We investigate vortex configurations with the “vulcanization” term inspired by the renormalization of ${\varphi }_{\star }^4$ theory in the canonical $\theta$-deformed noncommutativity. We focus on the classical limit of the theory described by a single parameter which is the ratio of the vulcanization and the noncommutativity parameters. We perform numerical calculations and find that nontopological vortex solutions exist as well as Q-ball type solutions, but topological vortex solutions are not admitted.

We consider supernova SN1987A to find bounds on the parameter of noncommutativity, ${\theta }_{\mu \nu }$. The right-handed neutrino in the noncommutative standard model (NCSM) can directly couple to the photon and the $Z$-gauge boson. Therefore the observed flux of neutrinos from SN1987A can constrain the strength of the new couplings in the NCSM. We obtain two bounds on the NC-parameter, ${\Lambda }_{\mathrm{NC}}=1/\sqrt{|}\theta |$, with respect to escaping or trapping of the right-handed neutrinos inside the supernova which are ${\Lambda }_{\mathrm{NC}}\gtrsim 3.7\mathrm{TeV}$ or ${\Lambda }_{\mathrm{NC}}\lesssim 1\mathrm{TeV}$, respectively. The excluded region $1\mathrm{TeV}\lesssim {\Lambda }_{\mathrm{NC}}\lesssim 3.7\mathrm{TeV}$ for the NC parameter is obtained for the first time. In fact ${\Lambda }_{\mathrm{NC}}\lesssim 1\mathrm{TeV}$ is consistent with the existing bounds on ${\Lambda }_{\mathrm{NC}}$ and raises our hopes to find the NC effects in the LHC or even in the LEP. Meanwhile ${\Lambda }_{\mathrm{NC}}\gtrsim 3.7\mathrm{TeV}$ is more stringent than the other bounds obtained from LEP and LHC considerations. Furthermore, since NC calculations are perturbative and are correct only up to the energy scale of the NC system $\lesssim {\Lambda }_{\mathrm{NC}}$, then these bounds (which are obtained from the energy scale and considerably less than the energy scale of LEP and LHC) are more reliable.

We present an analysis of the expected angular and distance uncertainties of spinning binary systems as measured by the space-based gravitational-wave observatory LISA. We focus on two distinct cases: supermassive coalescing black holes at high redshift and nearby binary star systems with roughly constant orbital frequency. We calculate the uncertainties using least-squares parameter estimation of simulated waveforms that are accurate to $4/2$ post-Newtonian order. Our results show that the presence of spin can decrease massive black hole distance and positional uncertainties by as much as factors of 10 and 100, respectively. In optimal circumstances, we find that LISA’s massive black hole merger resolution can be as low as ${10}^{-6}$ steradians. However, in low-mass binary systems the presence of spin tends to degrade LISA’s resolution by anywhere from a factor of 3 to a factor of 100.

The energy momentum tensor of a magnetic field always contains a spin-2 component in its anisotropic stress and therefore generates gravitational waves. It has been argued in the literature (Caprini and Durrer [C. Caprini and R. Durrer, Phys. Rev. D 65, 023517 (2001)]) that this gravitational wave production can be very strong and that backreaction cannot be neglected. On the other hand, a gravitational wave background does affect the evolution of magnetic fields. It has also been argued (Tsagas et al. [C. G. Tsagas, P. K. S. Dunsby, and M. Marklund, Phys. Lett. B 561, 17 (2003)] [C. Tsagas, Phys. Rev. D 72, 123509 (2005)]) that this can lead to a very strong amplification of a primordial magnetic field. In this paper we revisit these claims and study backreaction to second order.

In previous work on the quantum mechanics of an atom freely falling in a general curved background spacetime, the metric was taken to be sufficiently slowly varying on time scales relevant to atomic transitions that time derivatives of the metric in the vicinity of the atom could be neglected. However, when the time dependence of the metric cannot be neglected, it was shown that the Hamiltonian used there was not Hermitian with respect to the conserved scalar product. This Hamiltonian was obtained directly from the Dirac equation in curved spacetime. This raises the paradox of how it is possible for this Hamiltonian to be non-Hermitian. Here, we show that this non-Hermiticity results from a time dependence of the position eigenstates that enter into the Schrödinger wave function, and we write the expression for the Hamiltonian that is Hermitian for a general metric when the time dependence of the metric is not neglected.

The generalized second law (GSL) of black hole thermodynamics states that the sum of changes in black hole entropy and the ordinary entropy of matter and fields outside the hole must be non-negative. In the classical limit, the GSL reduces to Hawking’s area theorem. Neither law identifies the specific effects that make it work in particular situations. Motivated by Davies’ recent gedanken experiment he used to infer a bound on the size of the fine structure constant from the GSL, we study a series of variants in which an electric test charge is lowered to a finite radius and then dropped into a Schwarzschild, a near-extremal magnetic Reissner-Nordström or a near-extremal Kerr black hole. For a classical charge, we demonstrate that a specific “backreaction” effect is responsible for protecting the area theorem in the near-extremal examples. For the magnetically charged Reissner-Nordström hole an area theorem violation is defused by taking into account a subtle source of repulsion of the charge: the spinning up of the black hole in the process of bringing the charge down to its dropping point. In Kerr hole case, the electric self-force on the charge is sufficient to right matters. However, in all experiments involving an elementary charge, the full GSL would apparently be violated were the fine structure constant greater than about order unity. We argue that in this case a quantum effect, the Unruh-Wald quantum buoyancy, may protect the GSL.